There is no simple answer to this question, as you indicated, due to individual State variations, TCAS versions, RVSM or not, MEL, etc...
Once you've pushed back and started moving under your own power, MEL no longer applies, however, it may be prudent to refer to it regardless.
What you DO need to check prior to departure is whether or not you are allowed to ENTER airspace in each case, that can best be done by letting your OPS/FLIGHT PLANNING department run the flight plan again without TCAS installed and ascertain if this is mandatory. Engineering can assist in determining the MEL but is unaware of operational restrictions.